Convergence of Pseudocontractions and Applications to Two-stage and Asynchronous Multisplitting for Singular M -Matrices
Yangfeng Su, Amit Bhaya · SIAM Journal on Matrix Analysis and Applications · 2001
Pseudocontractions, which are generalizations of paracontractions in the linear case, are introduced in this paper in order to study the convergence of nonstationary iterative methods for linear systems in which the coefficient matrices are singular M-matrices. A general convergence theorem for pseudocontractions is developed. This theorem is used to analyze the convergence of two nonstationary parallel iterations: two-stage multisplitting iterations and asynchronous multisplitting iterations for singular M-matrices, without other contractivity conditions on the iteration matrices.